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Sharing a polluted river. (English) Zbl 1155.91449
Summary: A river carries pollutants to people living along it if it is polluted. To make the water in the river clean, some costs are incurred. This poses a question of how to split the costs of cleaning the whole river among the agents located along it. To answer this question, we resort to the two main advocated doctrines in international disputes: the theory of Absolute Territorial Sovereignty (ATS) and the theory of Unlimited Territorial Integrity (UTI). Applying these two doctrines, we accordingly propose two methods: the Local Responsibility Sharing (LRS) method and the Upstream Equal Sharing (UES) method. For each method, we provide an axiomatic characterization. Interestingly, both the LRS method and the UES method coincide with the Shapley value solutions to the corresponding (cost) games that are naturally induced according to the ATS and the UTI doctrines respectively.

91B76 Environmental economics (natural resource models, harvesting, pollution, etc.)
91A12 Cooperative games
91B32 Resource and cost allocation (including fair division, apportionment, etc.)
Full Text: DOI
[1] Ambec, S.; Sprumont, Y., Sharing a river, J. econ. theory, 107, 453-462, (2002) · Zbl 1033.91503
[2] Barret, S., 1994. Conflict and cooperation in managing international water resources. Working paper 1303. World Bank, Washington
[3] Boyd, J., 2003. Water pollution taxes: A good ideal doomed to failure, Discussion paper 03-20. Research for the Future, Washington
[4] Canterbury, E.R.; Marvasti, A., The coase theorem as a negative externality, J. econ. issues, 26, 1179-1189, (1992)
[5] Coase, R., The problem of social cost, J. law econ., 1, 1-14, (1960)
[6] Faulhaber, G., Cross-subsidization: pricing in public enterprises, Amer. econ. rev., 65, 966-977, (1975)
[7] Godana, B., Africa’s shared water resources, (1985), France Printer London
[8] Kilgour, M., Dinar A., 1996. Are stable agreements for sharing international river waters now possible? Working paper 1474. World Bank, Washington
[9] Moulin, H., Axioms of cooperative decision making, (1988), Cambridge Univ. Press · Zbl 0699.90001
[10] Moulin, H., Axiomatic cost and surplus sharing, () · Zbl 0536.90006
[11] Shapley, L.S., A value for n-person games, (), 307-317 · Zbl 0050.14404
[12] Tiebut, C., A pure theory of local expenditures, J. polit. economy, 64, 416-424, (1956)
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